Question: Rewrite as a simplified fraction. ${3.9\overline{65} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3965.6565...\\ 10x &= 39.6565...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3926}$ ${x = \dfrac{3926}{990}} $ ${x = \dfrac{1963}{495}} \text{or} {3 \dfrac{478}{495}}$